Method and systems for thumbnail generation, and corresponding computer program product

ABSTRACT

An embodiment of a consumer electronics product having a thumbnail display feature includes a system for generating and storing thumbnails having a given size from images, such as JPEG images, for which a spatial frequency domain representation is available. The system includes a zooming processor to reduce the size of the images by zooming. The zooming processor is configured to perform both spatial frequency domain zooming to approximate the desired thumbnail size and then image pixel domain zooming to fit the desired thumbnail size. The product includes cache storage configured to store a plurality of thumbnails in a file system as free blocks in the file system, so that file system data structures are left unchanged.

TECHNICAL FIELD

This disclosure relates to thumbnail generation.

This disclosure was devised by paying attention to its possible use in generating thumbnails for those images for which a representation is available in the spatial frequency domain; JPEG encoded images are exemplary of such images.

BACKGROUND

Thumbnail images (or, briefly, “thumbnails”) are small images derived from larger images by sub-sampling.

Generation of thumbnails is an ordinary feature of personal computers and a desired feature of other consumer electronic (CE) devices such as digital photo frames, digital cameras, mobile phones, multi-function printers, etc. These devices are equipped with a screen or other display unit allowing the user to preview and/or browse digital photos and digital pictures. Providing high-quality and short-time-consuming image thumbnail generation is quite helpful in these such devices. Digital photo previewing and browsing are exemplary of the applications involving decoding a digital image (typically in JPEG format) and resizing it in order to be displayed on a specific target screen, while taking into account quality and processing time constraints.

Generation of thumbnails is addressed extensively in the scientific and technical literature including the patent literature. WO-A-94/22108, US-A-2006/242163, and U.S. Pat. Nos. 6,263,119 and 6,778,707, which are incorporated by reference, are exemplary of patent documents related to thumbnail generation.

So far, two basic approaches have been resorted to for thumbnail generation.

A first approach involves a sub-sampling procedure in the image pixel domain. After choosing a zoom-out factor, based upon the relative dimensions of the target screen and the original image, data is filtered to obtain the desired resolution. To that end, resizing is performed through a line-by-line scanning, once the original image has been completely decoded (i.e., brought back to the image pixel domain), which inherently requires a considerable amount of computational time.

Another approach involves resolution scaling implemented using spatial frequency subsampling in the DCT or transform domain, during the image decoding step. For instance, a 8×8 DCT block can be sub-sampled using a scaling ratio selected out of {1, ½, ¼, ⅛} thus filtering out the high frequencies. Smaller scaling ratios permit significantly faster decoding since fewer coefficients need to be processed and a simpler IDCT method can be used. For instance, when choosing a ratio equal to ⅛, only the DC component is considered. The remainder of the decoding process, including the de-quantization of the quantized AC coefficients and the IDCT, can be “skipped”. Resizing may thus become a very fast process as the number of coefficients to be processed decreases, while, however, the final result may fail to optimally fit to the target screen and its shape (e.g., aspect ratio).

Additionally, certain systems such as certain embedded systems may not have sufficient memory resources to perform thumbnail caching as conventionally described in the literature, namely thumbnail caching into system mass storage (e.g., hard disk) or removable media (e.g., USB disk, SD card), which in any case involves writing files into the file system of the storage device. When removable mass-storage is used, if the media is abruptly removed during the write stage, file system corruption may occur.

SUMMARY

An embodiment of this disclosure provides an arrangement for generating image thumbnails without significant losses in quality while drastically reducing the processing time required.

Another embodiment of this disclosure provides an arrangement for generating image thumbnails that can be cached transparently in user mass storage devices.

An embodiment also relates to a corresponding system as well as a related computer program product, loadable in the memory of at least one computer and including software code portions for performing the steps of an embodiment of a method when the product is run on a computer. As used herein, reference to such a computer program product is intended to be equivalent to reference to a computer-readable medium containing instructions for controlling a computer system to coordinate the performance of a method embodiment. Reference to “at least one computer” is intended to highlight the possibility for an embodiment to be implemented in a distributed/modular fashion.

In an embodiment, a method is provided for the fast generation of a JPEG image thumbnail from the full-size JPEG image without producing visible quality deterioration.

In an embodiment, image-transition time on the screen of consumer electronics devices equipped with limited processing resources is reduced.

An embodiment reduces the image size to a target size by operating directly in the spatial frequency domain, during a decompression stage, by first bringing image size as close as possible to the target size; size refinement, to substantially perfectly match target size, is then performed by spatial sub-sampling and/or over-sampling. In comparison with conventional methods, a decompression stage takes much less time than full decompression since it operates only on certain frequencies, and at the same time reduces the original image size. Moreover, spatial resizing, when needed, processes a small amount of data.

In an embodiment, the image rendering time on a display device is reduced and made constant and independent of decoding time, by caching thumbnail data in a system memory (or in a user mass storage device, if the memory space available is insufficient, as may be the case in embedded systems). In an embodiment, this limitation is overcome by writing data (e.g., into user mass-storage) without changing its file system data structures. In comparison with conventional methods, writing thumbnail data without altering file system data structures preserves file system integrity threatened by asynchronous user storage media removal.

The arrangement herein provides high performance and is well suited for use in embedded systems and applications where image thumbnails are generated more often required than full images while computational resources are limited. Mobile and fixed consumer electronic devices (such as PDA, mobile phones, digital photo frames, multi-function printers) are exemplary of possible fields of use of this disclosure.

BRIEF DESCRIPTION OF THE DRAWINGS

One or more embodiments will now be described, by way of example only, with reference to the enclosed figures of drawing, wherein:

FIG. 1 is an embodiment of DCT coefficient selection in an embodiment;

FIG. 2 is an embodiment of a Thumbnails Cache Table (TCT); and

FIGS. 3 and 4 are block diagrams of embodiments of thumbnail caching arrangements.

DETAILED DESCRIPTION

In the following description, numerous specific details are given to provide a thorough understanding of embodiments. The embodiments can be practiced without one or more of the specific details, or with other methods, components, materials, etc. In other instances, well-known structures, materials, or operations are not shown or described in detail to avoid obscuring aspects of the embodiments.

Reference throughout this specification to “one embodiment” or “an embodiment” means that a particular feature, structure, or characteristic described in connection with the embodiment is included in at least one embodiment. Thus, the appearances of the phrases “in one embodiment” or “in an embodiment” in various places throughout this specification are not necessarily all referring to the same embodiment. Furthermore, the particular features, structures, or characteristics may be combined in any suitable manner in one or more embodiments.

The headings provided herein are for convenience only and do not limit the scope or meaning of the embodiments.

An embodiment “mixes” image resizing methods operating in the spatial frequency domain (e.g., based on discrete trigonometric transforms) with image resizing methods operating in the image pixel domain.

Assuming that I is the original size image, its thumbnail T can be represented by the following geometrical transformation

T=G(zoom,I)

where zoom is the computed ratio (smaller than unity) between thumbnail size and image size.

Since T (thumbnail) and I (image) may have different aspect ratios (i.e., the width-to-height ratio), and avoiding geometrical distortion may be advantageous, the parameter zoom is computed as:

min{(thumbnail_width/image_width), (thumbnail_height/image_height)} where min { } denotes the minimum of the two thumbnail-to-image width and height ratios.

In an embodiment, spatial frequency domain resizing is exploited to quickly move towards the target size and subsequently matching it by re-sampling the IDCT output.

Thus a zoom factor factorization is required, so that:

zoom=z ₁ ·z ₂

where

-   z₁ is the zoom factor used in the spatial frequency domain resizing     stage, and -   z₂ is the zoom factor used in the spatial (i.e., pixel) domain.

In addressing the issue of zoom factorization, it may be worth mentioning that spatial frequency zoom-out involves “power of two” factors i.e., 2^(k), so that valid values for z₁ are, e.g., in the set z₁={⅛, ¼, ½, 1}.

Zooming out by values in z₁ corresponds to considering the lower frequency portions of the image during the IDCT decoding step.

In particular, in the case of z₁={⅛, ¼, ½, 1} 1×1, 2×2, 4×4 and 8×8 (full) sub-blocks of DCT coefficients are taken into account, respectively. FIG. 1 shows IDCT filtering according to the corresponding DCT-coefficients-assembling technique.

In this case, zoom factorization is performed by selecting a value for z₁ out of the set {⅛, ¼, ½, 1}.

In the embodiment to which FIG. 1 refers, this selection is based on the following rule:

z ₁=1/k if (½k)<zoom≦(1/k)k=1, 2,4

z ₁=⅛ if zoom≦(⅛)

This rule leads to a z₂ zoom factor (calculated as z₂=zoom/z₁) which is smaller than or equal to one. This means that, when not already achieved (as is more often the case) via the z₁ zoom factor only, target size matching is achieved via further zoom-out via the z₂ zoom factor. In that case, the result of zoom-out via the z₁ zoom factor will in most instances be at least marginally “larger” than the target thumbnail size, so that further zoom-out via the z₂ zoom factor will be applied to achieve the desired matching to the target size.

It will be appreciated that a rule for selecting the z₁ zoom factor may be applied leading to a z₂ zoom factor which is larger than or equal to one. In that case, the result of zoom-out via the z₁ zoom factor will in most instances be at least marginally “smaller” than the target thumbnail size, so that further zoom-in via the z₂ zoom factor will be applied to achieve the desired matching to the target size.

For instance, in order to take further advantage of spatial frequency down-sampling, the z₁ function considered in the foregoing may be re-arranged as follows:

z ₁=1/k if (½qk)<zoom≦(1/qk) k=1, 2,4

z ₁=⅛ if zoom≦(1/q8)

where the parameter q can vary between {0.5, 1} and has the effect to expand and move the z₁ function in a geometric fashion.

In other words, under a specified threshold, the original image is zoomed out more than necessary. When this occurs, the z₂ zoom factor (again calculated as z₂=zoom/z₁) becomes larger than one, and a zoom-in processing is performed in order to achieve the desired target size.

The parameter q affects the trade-off between image degradation and time performance of the whole method.

Values for q close to 0.5 lead to time performance improvements (i.e., thumbnail generation is quicker), but introduce more image degradation in comparison with direct zooming, in that the image is first scaled down and then scaled up (other than in the case where zoom<⅛).

Conversely, values for q close to 1 typically do not introduce further image degradation, as in most cases, the image is only scaled down, but a less satisfactory time performance may ensue.

In both FIGS. 3 and 4, reference 10 denotes a processor module including zooming processor features for JPEG thumbnail generation as described in the foregoing. In an embodiment, such a processor is a conventional zooming processor including processing resources adapted to perform thumbnail generation according to the conventional methods discussed in the introductory portion of this disclosure.

In the embodiments considered, the processor 10 is included in a consumer electronics device CE (e.g., any of the consumer electronics devices discussed in the introductory portion of this description). The processor 10 is configured for interacting with a display unit 12 and a memory 14 for storing (caching) thumbnail data related to thumbnails to be displayed in the unit 12.

The processor 10 is programmed (in a manner known per se) to implement the zoom=z₁·z₂ processing discussed in the foregoing. Such zoom=z₁·z₂ processing entails advantages in terms of quality v. processing time/resources discussed previously.

Especially in low-capacity embedded systems, instantaneously refreshing images on an associated display device may be a critical factor. For that reason, once a first thumbnail has been generated, the processor 10 may generate (i.e., calculate) thumbnails in advance for display as soon as required: e.g., while a current picture is being displayed, “next” thumbnail data is generated in the background and cached into a system memory, ready to be displayed on demand.

As already indicated, certain embedded systems may not have sufficient memory resources to perform conventional thumbnail caching, while writing files into the file system of the storage device may result in corruption of the file system if the media is removed.

An embodiment considered herein is file system safe, in that it caches thumbnails into free blocks of the file system, without identifying them as allocated space. In this way, file-system data structures are never modified, so that integrity is always guaranteed. This can be successfully accomplished if no writing access chooses one of these occupied (by a thumbnail) blocks on the storage device in the meantime. For instance, this condition may be achieved when multitasking is not implemented.

In order to exemplify such an approach, one may think of generic file system metadata as a bitmap used to track allocated blocks. After volume creation, the bitmap will indicate that most blocks are free, typically having all bits clear. As the file system is used in write mode, the bitmap is updated to indicate used storage blocks. In order to find free space for thumbnails caching, the method is made file system aware (i.e., the bitmap is checked so that thumbnails are written to unoccupied blocks), so that user data corruption is avoided.

For instance, a fixed number of image thumbnails may be cached. Images to be cached are chosen in an application-specific manner. For instance, in the case of an application supporting image browsing in n-up mode, it could be useful to have 3n thumbnails cached for the current, previous, and next page. Conversely, if an application supports only a slide-show mode, then the very next photo is cached.

Once available free blocks have been found, a Thumbnail Cache Table (TCT) is allocated into the main memory. That table will be filled in and updated each time a new thumbnail is generated as shown in FIG. 2. There, the File_ID field represents a unique image file identifier (e.g., path/filename) and the First Block Address field represents a pointer to a first block of image thumbnail data.

FIGS. 3 and 4 are exemplary of two approaches for storing thumbnails in the memory 14.

In FIG. 3, each thumbnail is stored as a linked list of storage blocks (designated “data”).

The first bytes FB of each block are used as a pointer to the next one. The rest of the block is for data ended by EOF within the last block. The list is terminated with a special marker that is not a valid block number File_ID (FB=NULL for the last block in the list).

In FIG. 4, a tree-like arrangement is used where a first (“root”) block is used to store a sequence of pointers P1, P2, P3 to blocks of data.

If the first block is not enough to store all the block pointers, its last address is used to point to a second block of block pointers, and so on.

The sequence of pointers is ended with a special marker NULL that is not a valid block number. Again, the data is terminated with a special marker EOF.

The number of thumbnails that can be cached (and hence the number of entries in the thumbnail cache table) may be obtained as a parameter designated cached_thumbs by means of the following formula:

-   min{(free_disk space/thumbnail_size), -   (free_RAM_space/TCT_record_size), JPEG_files}

where min { } again denotes the minimum operator and where:

-   free_disk_space is the available space within user mass storage;     this may be calculated, e.g., by parsing the file system metadata; -   thumbnail_size is derived from the display resolution and its color     depth; this size takes into account also the block-pointers overhead     (i.e., the amount of memory occupied by the pointers FB or P1, . . .     , Pn); -   free_RAM_space represents the amount of free main memory that can be     dedicated to the allocation of Thumbnails Cache Table; -   TCT_record_size is the dimension of a single TCT entry; and -   JPEG_files is simply the number of pictures on the user mass     storage.

The number of cached_thumbs calculated as above can be possibly scaled down by other factors. For instance, the cache could be oversized if the processor has limited computation resources compared to application requirements, in which case the processor may be unable to fill the whole cache.

Without prejudice to the underlying principles of the disclosure, the details and the embodiments may vary, even appreciably, with respect to what has been described by way of example only, without departing from the spirit and scope of the disclosure.

Naturally, in order to satisfy local and specific requirements, a person skilled in the art may apply to the embodiments described above many modifications and alterations. Particularly, although one or more embodiments have been described with a certain degree of particularity, it should be understood that various omissions, substitutions, and changes in the form and details as well as other embodiments are possible. Moreover, it is expressly intended that specific elements and/or method steps described in connection with any disclosed embodiment may be incorporated in any other embodiment as a general matter of design choice. 

1. A method of generating a thumbnail having a given size from an image for which a spatial frequency domain representation is available, the method including reducing the size of said image by zooming, wherein said zooming involves both spatial frequency domain zooming to at least approximate said thumbnail given size and image pixel domain zooming to fit said thumbnail given size.
 2. The method of claim 1, wherein said image pixel domain zooming follows said spatial frequency domain zooming.
 3. The method of claim 2, wherein said spatial frequency domain zooming involves spatial frequency subsampling in the transform domain during image decoding, whereby said image pixel domain zooming is performed on the image resulting from said decoding.
 4. The method of claim 1, wherein said image pixel domain zooming includes zooming in to enlarge the result of said spatial frequency domain zooming.
 5. The method of claim 1, wherein said pixel domain zooming includes zooming out to reduce the result of said spatial frequency domain zooming.
 6. The method of claim 1, wherein said spatial frequency domain zooming involves zooming out said image by a power of two factor.
 7. The method of claim 1, wherein said spatial frequency domain zooming involves applying a zooming factor z₁ defined as follows: z ₁=1/k if (½qk)<zoom≦(1/qk) k=1, 2,4 z ₁=⅛ if zoom≦(1/q8) where: zoom is the overall zooming factor resulting from both said spatial frequency domain zooming and said pixel domain zooming, and q is a parameter selected in the interval {0.5, 1}.
 8. The method of claim 1, including caching a plurality of said thumbnails in a file system as free blocks in said file system, whereby file system data structures are left unchanged.
 9. The method of claim 1, including caching a plurality of said thumbnails as a linked list of storage blocks.
 10. The method of claim 9, wherein said linked list of storage blocks includes at least one block including a pointer to a next block in said linked list.
 11. The method of claim 1, including caching a plurality of said thumbnails in a tree-like arrangement.
 12. The method of claim 11, wherein said tree-like arrangement includes at least one block storing a sequence of pointers to other blocks in said tree-like arrangement.
 13. A method of caching thumbnails derived from respective images, including caching a plurality of said thumbnails in a file system as a free blocks in said file system, whereby file system data structures are left unchanged.
 14. The method of claim 13, including caching a plurality of said thumbnails as a linked list of storage blocks.
 15. The method of claim 14, wherein said linked list of storage blocks includes at least one block including a pointer to a next block in said linked list.
 16. The method of claim 13, including caching a plurality of said thumbnails in a tree-like arrangement.
 17. The method of claim 16, wherein said tree-like arrangement includes at least one block storing a sequence of pointers to other blocks in said tree-like arrangement.
 18. A method of generating and storing thumbnails having a given size, said thumbnails generated from images for which a spatial frequency domain representation is available, the method including reducing the size of said images by zooming, wherein said zooming involves both spatial frequency domain zooming to at least approximate said thumbnail given size and image pixel domain zooming to fit said thumbnail given size, the method comprising caching a plurality of said thumbnails in a file system as free blocks in said file system, whereby file system data structures are left unchanged.
 19. A system for generating thumbnails having a given size from images for which a spatial frequency domain representation is available, the system including a zooming processor to reduce the size of said images by zooming, wherein said zooming processor is configured to perform both spatial frequency domain zooming to at least approximate said thumbnail given size and image pixel domain zooming to fit said thumbnail given size.
 20. The system of claim 19, wherein said zooming processor is configured to perform said image pixel domain zooming following said spatial frequency domain zooming.
 21. The system of claim 20, wherein said zooming processor is configured to perform said spatial frequency domain zooming as spatial frequency subsampling in the transform domain during image decoding, whereby said zooming processor is configured to perform said image pixel domain zooming on images resulting from said decoding.
 22. The system of claim 19, wherein said zooming processor is configured to perform said image pixel domain zooming by zooming in to enlarge the result of said spatial frequency domain zooming.
 23. The system of claim 19, wherein said zooming processor is configured to perform said pixel domain zooming by zooming out to reduce the result of said spatial frequency domain zooming.
 24. The system of claim 19, wherein said zooming processor is configured to perform said spatial frequency domain zooming by zooming out said images by a power of two factor.
 25. The system of claim 19, wherein said zooming processor is configured to perform said spatial frequency domain zooming by applying a zooming factor z₁ defined as follows: z ₁=1/k if (½qk)<zoom≦(1/qk) k=1, 2,4 z ₁=⅛ if zoom≦(1/q8) where: zoom is the overall zooming factor resulting from both said spatial frequency domain zooming and said pixel domain zooming, and q is a parameter selected in the interval {0.5, 1}.
 26. The system of claim 19, including cache storage configured to store a plurality of said thumbnails in a file system as free blocks in said file system, whereby file system data structures are left unchanged.
 27. The system of claim 19, including cache storage configured to store a plurality of said thumbnails as a linked list of storage blocks.
 28. The system of claim 19, wherein said linked list of storage blocks in said cache storage includes at least one block including a pointer to a next block in said linked list.
 29. The system of claim 19, including cache storage configured to store a plurality of said thumbnails in a tree-like arrangement.
 30. The system of claim 29, wherein said tree-like arrangement in said cache storage includes at least one block storing a sequence of pointers to other blocks in said tree-like arrangement.
 31. A system for caching thumbnails derived from respective images, the system including cache storage configured to store a plurality of said thumbnails in a file system as a free blocks in said file system, whereby file system data structures are left unchanged.
 32. The system of claim 31, including cache storage configured to store a plurality of said thumbnails as a linked list of storage blocks.
 33. The system of claim 32, wherein said linked list of storage blocks in said cache storage includes at least one block including a pointer to a next block in said linked list.
 34. The system of claim 31, including cache storage configured to store a plurality of said thumbnails in a tree-like arrangement.
 35. The system of claim 34, wherein said tree-like arrangement in said cache storage includes at least one block storing a sequence of pointers to other blocks in said tree-like arrangement.
 36. A system for generating and storing thumbnails having a given size, said thumbnails generated from images for which a spatial frequency domain representation is available, the system including a zooming processor to reduce the size of said images by zooming, wherein said zooming processor is configured to perform both spatial frequency domain zooming to at least approximate said thumbnail given size and image pixel domain zooming to fit said thumbnail given size, the system including cache storage configured to store a plurality of said thumbnails in a file system as free blocks in said file system, whereby file system data structures are left unchanged.
 37. A consumer electronics product having a thumbnail display feature, the product including a system for generating thumbnails having a given size from images for which a spatial frequency domain representation is available, the system including a zooming processor to reduce the size of said images by zooming, wherein said zooming processor is configured to perform both spatial frequency domain zooming to at least approximate said thumbnail given size and image pixel domain zooming to fit said thumbnail given size.
 38. A consumer electronics product having a thumbnail display feature, the product including a system for caching thumbnails derived from respective images, the system including cache storage configured to store a plurality of said thumbnails in a file system as a free blocks in said file system, whereby file system data structures are left unchanged.
 39. A consumer electronics product having a thumbnail display feature, the product including a system for generating and storing thumbnails having a given size, said thumbnails generated from images for which a spatial frequency domain representation is available, the system including a zooming processor to reduce the size of said images by zooming, wherein said zooming processor is configured to perform both spatial frequency domain zooming to at least approximate said thumbnail given size and image pixel domain zooming to fit said thumbnail given size, the product including cache storage configured to store a plurality of said thumbnails in a file system as free blocks in said file system, whereby file system data structures are left unchanged.
 40. A computer program product loadable in the memory of at least one computer and including software code portions configured to be run on a computer in order to generate a thumbnail having a given size from an image for which a spatial frequency domain representation is available, said generating including reducing the size of said image by zooming, wherein said zooming involves both spatial frequency domain zooming to at least approximate said thumbnail given size and image pixel domain zooming to fit said thumbnail given size when the product is run on a computer
 41. A computer program product loadable in the memory of at least one computer and including software code portions configured to be run on a computer in order to cache thumbnails derived from respective images, including caching a plurality of said thumbnails in a file system as a free blocks in said file system, whereby file system data structures are left unchanged when the product is run on a computer.
 42. A computer program product loadable in the memory of at least one computer and including software code portions configured to be run on a computer in order to generate and store thumbnails having a given size, said thumbnails generated from images for which a spatial frequency domain representation is available, said generating including reducing the size of said image by zooming, wherein said zooming involves both spatial frequency domain zooming to at least approximate said thumbnail given size and image pixel domain zooming to fit said thumbnail given size, said storing including caching a plurality of said thumbnails in a file system as free blocks in said file system, whereby file system data structures are left unchanged when the product is run on a computer
 43. A method, comprising: scaling an encoded image by changing by a first factor at least one dimension of transform-domain blocks that represent the encoded image; decoding the scaled encoded image; and scaling the decoded image by changing by a second factor at least one dimension of the decoded image.
 44. The method of claim 43 wherein the first and second factors are different.
 45. The method of claim 43 wherein at least one of the first and second factors equals unity.
 46. The method of claim 43 wherein the first and second factors are greater than unity.
 47. The method of claim 43 wherein the first and second factors are less than unity.
 48. The method of claim 43 wherein: one of the first and second factors is greater than unity; and the other of the first and second factors is less than unity.
 49. The method of claim 43 wherein scaling the encoded image comprises changing at least two dimensions of the transform-domain blocks by the first factor.
 50. The method of claim 43 wherein scaling the decoded image comprises changing at least two dimensions of the decoded image by the second factor.
 51. The method of claim 43 wherein scaling the encoded image comprises reducing by the first factor the at least one dimension of the transform-domain blocks, the at least one dimension being an integer multiple of the first factor.
 52. The method of claim 43 wherein scaling the encoded image comprises reducing by the first factor at least two dimensions of the transform-domain blocks, the at least two dimensions being respective integer multiples of the first factor.
 53. The method of claim 43 wherein changing by the first factor at least one dimension of the transform-domain blocks comprises changing by the first factor a number of transform coefficients along the at least one dimension, the number of transform coefficients being an integer multiple of the first factor.
 54. A processor operable: to scale an encoded image by changing by a first factor at least one dimension of transform-domain blocks that represent the encoded image; to decode the scaled encoded image; and to scale the decoded image by changing by a second factor at least one dimension of the decoded image.
 55. A processor operable: to scale an encoded image by changing by a first factor at least one dimension of transform-domain blocks that represent the encoded image; to decode the scaled encoded image; and to scale the decoded image by changing by a second factor at least one dimension of the decoded image.
 56. A system, comprising: a memory; and a processor coupled to the memory and operable to scale an encoded image by changing by a first factor at least one dimension of transform-domain blocks that represent the encoded image, to decode the scaled encoded image, and to scale the decoded image by changing by a second factor at least one dimension of the decoded image.
 57. The system of claim 56 wherein the memory and the processor are disposed on a same integrated-circuit die.
 58. The system of claim 56 wherein the memory and the processor are disposed on respective integrated-circuit dies.
 59. A method, comprising: storing in a first memory location an image identifier and a pointer to a second memory location; and storing in the second memory location a pointer to a third memory location that stores at least a first portion of the image corresponding to the image identifier.
 60. The method of claim 59, further comprising storing in the second memory location at least a second portion of the image corresponding to the image identifier.
 61. The method of claim 59, further comprising storing in the second memory location a pointer to a fourth memory location that stores at least a second portion of the image.
 62. The method of claim 59, further comprising storing in the third memory location a pointer to a fourth memory location that stores at least a second portion of the image.
 63. The method of claim 59, further comprising storing in the second memory location a pointer to a fourth memory location that stores at least a second portion of the image and a value indicating an end of the image.
 64. The method of claim 59, further comprising storing in the second memory location a pointer to a fourth memory location that stores a value indicating an end of the image.
 65. The method of claim 59, further comprising storing in the second memory location after the pointer a value indicating that there are no additional pointers in the second memory.
 66. The method of claim 59, further comprising storing in the third memory location a pointer that points to a fourth memory location via at least one other memory location, the fourth memory location storing a value indicating an end of the image.
 67. The method of claim 59, further comprising storing in the third memory location a pointer that points to a fourth memory location via at least one other memory location, the fourth memory location storing at least a second portion of the image and a value indicating an end of the image.
 68. A system, comprising: a memory; a processor coupled to the memory and operable to store in a first location of the memory an image identifier and a pointer to a second location of the memory; and to store in the second location of the memory a pointer to a third location of the memory that stores at least a first portion of the image corresponding to the image identifier.
 69. The system of claim 68 wherein the memory and the processor are disposed on a same integrated-circuit die.
 70. The system of claim 68 wherein the memory and the processor are disposed on respective integrated-circuit dies. 